I beg to differ: D&D is fairly precise in its description of magic and any modification is Dungeon Master house rule. This kind of magic is used in even higher fantasy settings, like The Inheritance Cycle (Eragon...Inheritance) or the Wizards (written by Mikael Peinkofer, it had a very small success in fact the third book isn't translated nor sold outside its native Germany and I can't find the second book even online).

Also I'm pretty sure I read this kind of depiction elsewhere but I can't remember the sources. Not even The Dresden Files, which is VERY HIGH magic, uses this paradigm unless mitivated, Jim Butcher tends to be fairly scientific in its use of magic (he uses what in D&D would be Conjuration, even for its "Evocation" style, and it makes sense).

Also Low Magic scenarios tend to represent magic as either a huge arcane world-changing force in the hand of a handful of strange subjects or as small tricks that do not work as often as they do. In these scenarios strage things like blue fires or strange lightings are pretty standard, as magic is an "outside" force, a breach in the fabric of reality.

Personally, I really like it when the magic is connected to the temper / nature of the wizard, it adds to the flavor of the character and sets a general atmosphere. And a good character atmosphere is hard to create but so easily shattered

With the danger of sounding like some fashion guy: A sea wizard's spells for example should never have a red or yellow color, its just....wrong!

I said low fantasy, not low magic. That's a genre. Not the same thing.

And I'm talking about D&D as a whole. Not about some specific book or version. My experience of D&D has always been the same during the past decades, and I've been a D&D player. What's absolutely certain though, is that I'm not referring to the current edition, you can believe that. But I do trust players to always go over the top

But basically, your description could fit, yes: magic either changes the world or does nothing.
Add one element : Sorcery is repulsive. I keep thinking about that "Gelid Bones" spell from the Conan RPG. You can pretty much guess what it does.